Global optimization of univariate Lipschitz functions: II. New algorithms and computational comparison

We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b]. Problem P: find a globally-optimal value off and a corresponding point; Problem Q: find a set of disjoint subintervals of [a, b] containing only points with a globally-optimal value and the union of which contains all globally optimal points. A two-phase algorithm is proposed for Problem P. In phase I, this algorithm obtains rapidly a solution which is often globally-optimal. Moreover, a sufficient condition onf for this to be the case is given. In phase II, the algorithm proves the-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globally-optimal value. The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen. For small, the new algorithm requires only a few percent more function evaluations than the best possible one. An extended version of Piyavskii's algorithm is proposed for problem Q. A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals. This result is achieved for all twenty test problems.The research of the authors has been supported by AFOSR grants 0271 and 0066 to Rutgers University. Research of the second author has been also supported by NSERC grant GP0036426, FCAR grant 89EQ4144 and partially by AFOSR grant 0066. We thank Nicole Paradis for her help in drawing the figures.     

Capture by stabilized continuum: Classical and quantum aspects

We review here the results of our investigations concerning chaotic atomic scattering in the presence of a laser field. Particular emphasis is put on the existence of classical stable resonance structures, induced by the intense laser field, which are embedded in the field-free continuum. We show that phase space structures in the vicinity of a resonance island play an important role in the chaotic scattering behavior and form the basis for a mechanism to enhance the lifetimes of the collisional partners. Quantum calculations, based on a wave packet propagation method, show that quantum solutions are strongly influenced by the classical phase space structures. More specifically, a wave packet is found to spread differently in the regular and chaotic regions; in the latter case it spreads exponentially with time until saturation occurs, defining the saturation time. We also investigate the dependence of the spreading rates in both the regular and chaotic regimes. Calculations with an ensemble of classical trajectories are also presented to further illustrate the smoothing effects of varying.     

An Efficient Method for the Synthesis of Acyl-diazenes Using NaNO_2/NaHSO_4·H_2O

Azo compounds are widely utilized as analytic reagents and dyes1, they can also be used in material of non-linear optics, material of optics information storing in laser disks, and dyes with oil solubility in photochromy in modern technology2. Recently, many noteworthy studies have shown that some azo compounds possess excellent optical memory and photoelectric properties3,4. For example, polymer scaffolds bearing azobenzene-potential are useful for optical information storage, azo-dye doped…     

月桂树叶中蛋白质的提取工艺研究

桂花(Osmanthus fragrans Lour)是木犀属植物,原产我国,属我国传统十大名花之一,素以香花著称.桂花喜湿润,亦耐旱;喜阳光,亦耐阴;喜温暖,亦耐寒[1].叶是植物进行光合作用和蒸腾作用的主要部位,与周围环境有密切关系.桂花叶形较小,革质.     

A study of a nonprimitive model for electrolyte solutions based on perturbation theory

The equation for the Helmholtz free energy for systems of small anisotropic molecules and ions is deduced by substituting the complete expression for various potential energies (including repulsive, dispersive, electrostatic, and induced energies) into the perturbation expansion. The equation is applied to pure water. The relative dielectric constant is set at unity. Based on the equal chemical potentials of equilibrated vapor and liquid phases, the molecular parameters of water are regressed from the densities of saturated vapor in the temperature range of 0 to 370°C. The ARD of regression is 1.16%. These parameters are used to predict the heat of vaporization and densities of saturated vapor and liquid phases of water in the same temperature range. The ARDs of prediction are 4.5% and 9.8%, respectively. The equation is used to correlate the osmotic coefficients of twelve 1:1 electrolyte solutions. The relative dielectric constant is set at unity. The parameters (Soft-sphere diameter and dispersive constant) of seven ions (Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, and I^–) are obtained. The total average absolute deviation between calculated and experimental values of the osmotic coefficient is 0.041. The parameters of ions can keep constant in different systems.     

Rapid chiral analysis based on liquid-phase cyclic chemiluminescence

Rapid chiral analysis has become one of the important aspects of academic and industrial research. Here we describe a new strategy based on liquid-phase cyclic chemiluminescence (CCL) for rapid resolution of enantiomers and determination of enantiomeric excess (ee). A single CCL measurement can acquire multistage signals that provide a unique way to examine the intermolecular interactions between chiral hosts and chiral guests, because the lifetime (τ) of the multistage signals is a concentration-independent and distinguishable constant for a given chiral host–guest system. According to the τ values, CCL allows discrimination between a wide range of enantiomeric pairs including chiral alcohols, amines and acids by using only one chiral host. Even the chiral systems hardly distinguished by nuclear magnetic resonance and fluorescence methods can be distinguished easily by CCL. Additionally, the τ value of a mixture of two enantiomers is equal to the weighted average of each enantiomer, which can be used for the direct determination of ee without the need to separate the chiral mixture and create calibration curves. This is extremely crucial for the cases without readily available enantiomerically pure samples. This strategy was successfully applied to monitoring of the Walden inversion reaction and analysis of chiral drugs. The results were in good agreement with those obtained by high-performance liquid chromatography, indicating the utility of CCL for routine quick ee analysis. Mechanism study revealed that the τ value is possibly related to the activity of the chiral substance to catalyze a luminol–H₂O₂ reaction. Our research provides an unprecedented and general protocol for chirality differentiation and ee determination, which is anticipated to be a useful technology that will find wide application in chirality-related fields, particularly in asymmetric synthesis and the pharmaceutical industry.

Rapid chiral analysis has become one of the important aspects of academic and industrial research.